diff --git a/draft.tex b/draft.tex index bf4151a..627ff81 100644 --- a/draft.tex +++ b/draft.tex @@ -119,7 +119,7 @@ \allowdisplaybreaks \preprint{ZU-TH-} -\title{Towards establishing Lepton Flavour Universality breaking in $B\to K^*\ell^+\ell^-$ decays} +\title{Towards establishing Lepton Flavour Universality breaking in $\bar{B}\to \bar{K}^*\ell^+\ell^-$ decays} %\title{Novel approach for probing Lepton Flavour Universality in $B\to K^*\ell^+\ell^-$ decays} %\title{Probing Lepton Flavour Universality in $B\to K^*\ell^+\ell^-$ decays} \author{Andrea Mauri} @@ -131,13 +131,74 @@ \affiliation{Physik-Institut, Universit\"at Z\"urich, Winterthurer Strasse 190, 8057 Z\"urich, Switzerland} \begin{abstract} - Abstract + Rare semileptonic $b \to s \ell^+ \ell^-$ transitions provide some of the most promising framework to search for New Physics effects. + Recent analyses have indicated an anomalous pattern in measurements of lepton-flavour-universality observables. + We propose a novel approach to independently and complementary clarify the nature of these effects + by performing a simultaneous amplitude analysis of $B^0 \to K^{*0} \mu^+\mu^-$ and $B^0 \to K^{*0} e^+e^-$ decays. + This method enables the direct determination of the difference of the Wilson Coefficients ${\cal{C}}_{9}$ and ${\cal{C}}_{10}$ between electrons and muons, + and are found to be insensitive to both local and non-local hadronic contributions. + We show that considering the current preferred New Physics scenario a first observation of LFU breaking in a single measurement is possible with LHCb Run-II dataset. \end{abstract} \maketitle +Flavour change neutral current processes of {\textit{B}} meson decays, dominantly mediated by +$b \to s$ amplitudes, are crucial probes for the Standard Model (SM), +since as-yet undiscovered particles may contribute to loop effects and cause observables to deviate +from their SM predictions~\cite{Grossman:1996ke,Fleischer:1996bv,London:1997zk,Ciuchini:1997zp}. +The decay mode $\bar{B}\to \bar{K}^*\ell^+\ell^-$ is a prime example (\textit{i.e.} $\ell = \mu, e$), +which offers a rich framework to study from differential decay widths to angular observables. +An anomalous behaviour in angular and branching fraction analyses of the decay channel +$B^{0} \to K^{*0} \mu^{+}\mu^{-}$ has been recently reported~\cite{Aaij:2015oid,Wehle:2016yoi,Aaij:2013aln,Aaij:2014pli}, +notably in one of the observables with reduced form-factor uncertainties, +$P^{\prime}_{5}$~\cite{Descotes-Genon:2015uva}. +Several models have been suggested in order to interpret these results as New Physics (NP) +signatures~\cite{Gauld:2013qja,Buras:2013qja,Altmannshofer:2013foa,Crivellin:2015era,Hiller:2014yaa,Biswas:2014gga,Gripaios:2014tna}. +Nonetheless, the vector-like nature of this pattern could be also explained by +large hadronic contributions from $b\to s c{\bar{c}}$ operators ({\textit{i.e.}} charm loops) +that are able to either mimic or camouflage NP effects~\cite{Jager:2012uw,Jager:2014rwa}. +Non-standard measurement in ratios of $b \to s \ell^+ \ell^-$ processes +- such as of $R_{K}$~\cite{Aaij:2014ora} and $R_{K^{*}}$~\cite{Aaij:2017vbb} - +indicate a suppression of the muon channel which is also compatible with the $P^{\prime}_{5}$ anomaly. +In this case an immediate interpretation of lepton flavour universality (LFU) breaking is +suggested due to the small theoretical uncertainties in their predictions~\cite{Hiller:2003js,Bordone:2016gaq}. +Whilst the individual level of significance of the present anomalies is still inconclusive, +there is an appealing non-trivial consistency shown in +global analysis fits~\cite{Capdevila:2017bsm,Altmannshofer:2017yso,Hurth:2017hxg}. -In this work we assume the $\Bz \to \Kstarz \ellell$ decay being completely dominated +The formalism of {\textit{b}} decays is commonly described within +an effective field theory~\cite{Altmannshofer:2008dz} - +hereafter only a subset of the Wilson coefficients $C_i$ for the basis of +dimension-six field operators $O_i$ is used for the weak Lagrangian~\cite{Bobeth:2017vxj}. +In this framework NP effects are systematically incorporated +by introducing deviations exclusively in the Wilson coefficients (WC)~\cite{Ali:1994bf} +({\textit{i.e.}} $\mathcal{C}_i = \mathcal{C}^{\mathrm{SM}}_i + \mathcal{C}^{\mathrm{NP}}_i$). +%For instance, whilst the individual level of significance of the present anomalies is still inconclusive, +%there is an appealing non-trivial consistency shown in +%global analysis fits~\cite{Capdevila:2017bsm,Altmannshofer:2017yso,Hurth:2017hxg}; +%\textit{i.e.} a shift in the coefficient $\mathcal{C}_9$ only, +%or $\mathcal{C}_9$ and $\mathcal{C}_{10}$ simultaneously. +For instance, the anomalous pattern seen in semileptonic decays can be +explained by a shift in the coefficient $\mathcal{C}_9$ only, +or $\mathcal{C}_9$ and $\mathcal{C}_{10}$ simultaneously. +A direct experimental determination of the WCs is currently +bounded by sizeable uncertainties that arise from +non-factorisable hadronic contributions. +Some promising approaches propose to either extract these non-local hadronic elements +from data-driven analyses~\cite{Blake:2017fyh,Hurth:2017sqw} +or by using the analytical and dispersive properties of these correlators~\cite{Bobeth:2017vxj}. +However these models still have intrinsic limitations, in particular +in the assumption of the parametrisation of the di-lepton invariant mass. + +In this letter we propose a new \textit{model-independent} approach that +from a simultaneous amplitude analysis of both +$B^0 \to K^{*0} \mu^+\mu^-$ and $B^0 \to K^{*0} e^+e^-$ decays +can, for the first time, unambiguously determine LFU-breaking from direct measurements of WCs. +Furthermore, in this method the full set of observables available in $\bar{B}\to \bar{K}^*\ell^+\ell^-$ +decays is exploited, and therefore, most stringent constraints on LFU are expected. + +% Start of proper paper discussion +In this work we assume the $\bar{B}\to \bar{K}^*\ell^+\ell^-$ decay being completely dominated by the on-shell $\Kstarz$ ($p$-wave) contribution. The differential decay rate is hence fully described by four kinematic variables: the di-lepton invariant mass square, $q^2$, and the three angles $\vec{\Omega} = (\cos \theta_l, \cos \theta_K, \phi)$ [Ref]. diff --git a/references.bib b/references.bib new file mode 100644 index 0000000..4e00960 --- /dev/null +++ b/references.bib @@ -0,0 +1,458 @@ +@article{Grossman:1996ke, + author = "Grossman, Yuval and Worah, Mihir P.", + title = "{CP asymmetries in B decays with new physics in decay + amplitudes}", + journal = "Phys.Lett.", + volume = "B395", + pages = "241-249", + doi = "10.1016/S0370-2693(97)00068-3", + year = "1997", + eprint = "hep-ph/9612269", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "SLAC-PUB-7351", + SLACcitation = "%%CITATION = HEP-PH/9612269;%%", +} +@article{Fleischer:1996bv, + author = "Fleischer, Robert", + title = "{CP violation and the role of electroweak penguins in + nonleptonic $B$ decays}", + journal = "Int. J. Mod. Phys.", + volume = "A12", + year = "1997", + pages = "2459-2522", + doi = "10.1142/S0217751X97001432", + eprint = "hep-ph/9612446", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "TTP-96-58, TTP96-58", + SLACcitation = "%%CITATION = HEP-PH/9612446;%%" +} +@article{London:1997zk, + author = "London, David and Soni, Amarjit", + title = "{Measuring the CP angle $\beta$ in hadronic $b \to s$ penguin decays}", + journal = "Phys.Lett.", + volume = "B407", + pages = "61-65", + doi = "10.1016/S0370-2693(97)00695-3", + year = "1997", + eprint = "hep-ph/9704277", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "UDEM-GPP-TH-97-40", + SLACcitation = "%%CITATION = HEP-PH/9704277;%%", +} +@article{Ciuchini:1997zp, + author = "Ciuchini, Marco and Franco, E. and Martinelli, G. and + Masiero, A. and Silvestrini, L.", + title = "{CP violating B decays in the standard model and + supersymmetry}", + journal = "Phys.Rev.Lett.", + volume = "79", + pages = "978-981", + doi = "10.1103/PhysRevLett.79.978", + year = "1997", + eprint = "hep-ph/9704274", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "CERN-TH-97-047, CERN-TH-97-47, ROM2F-97-10", + SLACcitation = "%%CITATION = HEP-PH/9704274;%%", +} +@article{Altmannshofer:2008dz, + author = "Altmannshofer, Wolfgang and Ball, Patricia and Bharucha, + Aoife and Buras, Andrzej J. and Straub, David M. and Wick, + Michael", + title = "{Symmetries and Asymmetries of $B \to K^{*} \mu^{+} + \mu^{-}$ Decays in the Standard Model and Beyond}", + journal = "JHEP", + volume = "01", + year = "2009", + pages = "019", + doi = "10.1088/1126-6708/2009/01/019", + eprint = "0811.1214", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "IPPP-08-58, DCPT-08-116, TUM-HEP-696-08", + SLACcitation = "%%CITATION = ARXIV:0811.1214;%%" +} +@article{Ali:1994bf, + author = "Ali, Ahmed and Giudice, G. F. and Mannel, T.", + title = "{Towards a model independent analysis of rare $B$ + decays}", + journal = "Z. Phys.", + volume = "C67", + year = "1995", + pages = "417-432", + doi = "10.1007/BF01624585", + eprint = "hep-ph/9408213", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "CERN-TH-7346-94", + SLACcitation = "%%CITATION = HEP-PH/9408213;%%" +} +@article{Aaij:2015oid, + author = "Aaij, Roel and others", + title = "{Angular analysis of the $B^{0} \to K^{*0} \mu^{+} + \mu^{-}$ decay using 3 fb$^{-1}$ of integrated + luminosity}", + collaboration = "LHCb", + journal = "JHEP", + volume = "02", + year = "2016", + pages = "104", + doi = "10.1007/JHEP02(2016)104", + eprint = "1512.04442", + archivePrefix = "arXiv", + primaryClass = "hep-ex", + reportNumber = "CERN-PH-EP-2015-314, LHCB-PAPER-2015-051", + SLACcitation = "%%CITATION = ARXIV:1512.04442;%%" +} + +@article{Descotes-Genon:2015uva, + author = "Descotes-Genon, Sébastien and Hofer, Lars and Matias, + Joaquim and Virto, Javier", + title = "{Global analysis of $b\to s\ell\ell$ anomalies}", + journal = "JHEP", + volume = "06", + year = "2016", + pages = "092", + doi = "10.1007/JHEP06(2016)092", + eprint = "1510.04239", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "LPT-ORSAY-15-68, QFET-2015-29, SI-HEP-2015-19", + SLACcitation = "%%CITATION = ARXIV:1510.04239;%%" +} + +@article{Wehle:2016yoi, + author = "Wehle, S. and others", + title = "{Lepton-Flavor-Dependent Angular Analysis of $B\to K^\ast + \ell^+\ell^-$}", + collaboration = "Belle", + year = "2016", + eprint = "1612.05014", + archivePrefix = "arXiv", + primaryClass = "hep-ex", + reportNumber = "BELLE-PREPRINT-2016-15, KEK-PREPRINT-2016-54", + SLACcitation = "%%CITATION = ARXIV:1612.05014;%%" +} +@article{Gauld:2013qja, + author = "Gauld, Rhorry and Goertz, Florian and Haisch, Ulrich", + title = "{An explicit Z'-boson explanation of the $B \to K^* \mu^+ + \mu^-$ anomaly}", + journal = "JHEP", + volume = "01", + year = "2014", + pages = "069", + doi = "10.1007/JHEP01(2014)069", + eprint = "1310.1082", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + SLACcitation = "%%CITATION = ARXIV:1310.1082;%%" +} +@article{Buras:2013qja, + author = "Buras, Andrzej J. and Girrbach, Jennifer", + title = "{Left-handed $Z'$ and $Z$ FCNC quark couplings facing new + $b \to s \mu^+ \mu^-$ data}", + journal = "JHEP", + volume = "12", + year = "2013", + pages = "009", + doi = "10.1007/JHEP12(2013)009", + eprint = "1309.2466", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "FLAVOUR(267104)-ERC-50", + SLACcitation = "%%CITATION = ARXIV:1309.2466;%%" +} +@article{Altmannshofer:2013foa, + author = "Altmannshofer, Wolfgang and Straub, David M.", + title = "{New Physics in $B \to K^*\mu\mu$?}", + journal = "Eur. Phys. J.", + volume = "C73", + year = "2013", + pages = "2646", + doi = "10.1140/epjc/s10052-013-2646-9", + eprint = "1308.1501", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "FERMILAB-PUB-13-310-T, MITP-13-047", + SLACcitation = "%%CITATION = ARXIV:1308.1501;%%" +} +@article{Crivellin:2015era, + author = "Crivellin, Andreas and Hofer, Lars and Matias, Joaquim + and Nierste, Ulrich and Pokorski, Stefan and Rosiek, + Janusz", + title = "{Lepton-flavour violating $B$ decays in generic $Z'$ + models}", + journal = "Phys. Rev.", + volume = "D92", + year = "2015", + number = "5", + pages = "054013", + doi = "10.1103/PhysRevD.92.054013", + eprint = "1504.07928", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "CERN-PH-TH-2015-091, TTP15-018", + SLACcitation = "%%CITATION = ARXIV:1504.07928;%%" +} +# Leptoquarks +@article{Hiller:2014yaa, + author = "Hiller, Gudrun and Schmaltz, Martin", + title = "{$R_K$ and future $b \to s \ell \ell$ physics beyond the + standard model opportunities}", + journal = "Phys. Rev.", + volume = "D90", + year = "2014", + pages = "054014", + doi = "10.1103/PhysRevD.90.054014", + eprint = "1408.1627", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "DO-TH-14-17", + SLACcitation = "%%CITATION = ARXIV:1408.1627;%%" +} +@article{Biswas:2014gga, + author = "Biswas, Sanjoy and Chowdhury, Debtosh and Han, Sangeun + and Lee, Seung J.", + title = "{Explaining the lepton non-universality at the LHCb and + CMS within a unified framework}", + journal = "JHEP", + volume = "02", + year = "2015", + pages = "142", + doi = "10.1007/JHEP02(2015)142", + eprint = "1409.0882", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + SLACcitation = "%%CITATION = ARXIV:1409.0882;%%" +} +@article{Gripaios:2014tna, + author = "Gripaios, Ben and Nardecchia, Marco and Renner, S. A.", + title = "{Composite leptoquarks and anomalies in $B$-meson + decays}", + journal = "JHEP", + volume = "05", + year = "2015", + pages = "006", + doi = "10.1007/JHEP05(2015)006", + eprint = "1412.1791", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + SLACcitation = "%%CITATION = ARXIV:1412.1791;%%" +} +# QCD issues +@article{Jager:2012uw, + author = "Jäger, S. and Martin Camalich, J.", + title = "{On $B \to V \ell \ell$ at small dilepton invariant + mass, power corrections, and new physics}", + journal = "JHEP", + volume = "05", + year = "2013", + pages = "043", + doi = "10.1007/JHEP05(2013)043", + eprint = "1212.2263", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + SLACcitation = "%%CITATION = ARXIV:1212.2263;%%" +} +@article{Jager:2014rwa, + author = "Jäger, Sebastian and Martin Camalich, Jorge", + title = "{Reassessing the discovery potential of the $B \to K^{*} + \ell^+\ell^-$ decays in the large-recoil region: SM + challenges and BSM opportunities}", + journal = "Phys. Rev.", + volume = "D93", + year = "2016", + number = "1", + pages = "014028", + doi = "10.1103/PhysRevD.93.014028", + eprint = "1412.3183", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + SLACcitation = "%%CITATION = ARXIV:1412.3183;%%" +} +@article{Aaij:2014ora, + author = "Aaij, Roel and others", + title = "{Test of lepton universality using $B^{+}\rightarrow + K^{+}\ell^{+}\ell^{-}$ decays}", + collaboration = "LHCb", + journal = "Phys. Rev. Lett.", + volume = "113", + year = "2014", + pages = "151601", + doi = "10.1103/PhysRevLett.113.151601", + eprint = "1406.6482", + archivePrefix = "arXiv", + primaryClass = "hep-ex", + reportNumber = "CERN-PH-EP-2014-140, LHCB-PAPER-2014-024", + SLACcitation = "%%CITATION = ARXIV:1406.6482;%%" +} +@article{Aaij:2017vbb, + author = "Aaij, R. and others", + title = "{Test of lepton universality with $B^{0} \rightarrow + K^{*0}\ell^{+}\ell^{-}$ decays}", + collaboration = "LHCb", + journal = "JHEP", + volume = "08", + year = "2017", + pages = "055", + doi = "10.1007/JHEP08(2017)055", + eprint = "1705.05802", + archivePrefix = "arXiv", + primaryClass = "hep-ex", + reportNumber = "LHCB-PAPER-2017-013, CERN-EP-2017-100", + SLACcitation = "%%CITATION = ARXIV:1705.05802;%%" +} +% BR measurements +@article{Aaij:2013aln, + author = "Aaij, R and others", + title = "{Differential branching fraction and angular analysis of + the decay $B_s^0\to\phi\mu^{+}\mu^{-}$}", + collaboration = "LHCb", + journal = "JHEP", + volume = "07", + year = "2013", + pages = "084", + doi = "10.1007/JHEP07(2013)084", + eprint = "1305.2168", + archivePrefix = "arXiv", + primaryClass = "hep-ex", + reportNumber = "CERN-PH-EP-2013-078, LHCB-PAPER-2013-017", + SLACcitation = "%%CITATION = ARXIV:1305.2168;%%" +} +@article{Aaij:2014pli, + author = "Aaij, R. and others", + title = "{Differential branching fractions and isospin asymmetries + of $B \to K^{(*)} \mu^+ \mu^-$ decays}", + collaboration = "LHCb", + journal = "JHEP", + volume = "06", + year = "2014", + pages = "133", + doi = "10.1007/JHEP06(2014)133", + eprint = "1403.8044", + archivePrefix = "arXiv", + primaryClass = "hep-ex", + reportNumber = "LHCB-PAPER-2014-006, CERN-PH-EP-2014-055", + SLACcitation = "%%CITATION = ARXIV:1403.8044;%%" +} +@article{Hiller:2003js, + author = "Hiller, Gudrun and Kruger, Frank", + title = "{More model-independent analysis of $b \to s$ processes}", + journal = "Phys. Rev.", + volume = "D69", + year = "2004", + pages = "074020", + doi = "10.1103/PhysRevD.69.074020", + eprint = "hep-ph/0310219", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "LMU-18-03, TUM-HEP-519-03", + SLACcitation = "%%CITATION = HEP-PH/0310219;%%" +} +@article{Bordone:2016gaq, + author = "Bordone, Marzia and Isidori, Gino and Pattori, Andrea", + title = "{On the Standard Model predictions for $R_K$ and + $R_{K^*}$}", + journal = "Eur. Phys. J.", + volume = "C76", + year = "2016", + number = "8", + pages = "440", + doi = "10.1140/epjc/s10052-016-4274-7", + eprint = "1605.07633", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + SLACcitation = "%%CITATION = ARXIV:1605.07633;%%" +} +@article{Capdevila:2017bsm, + author = "Capdevila, Bernat and Crivellin, Andreas and + Descotes-Genon, Sébastien and Matias, Joaquim and Virto, + Javier", + title = "{Patterns of New Physics in $b\to s\ell^+\ell^-$ + transitions in the light of recent data}", + journal = "JHEP", + volume = "01", + year = "2018", + pages = "093", + doi = "10.1007/JHEP01(2018)093", + eprint = "1704.05340", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "PSI-PR-17-05, LPT-ORSAY-17-19", + SLACcitation = "%%CITATION = ARXIV:1704.05340;%%" +} +@article{Altmannshofer:2017yso, + author = "Altmannshofer, Wolfgang and Stangl, Peter and Straub, + David M.", + title = "{Interpreting Hints for Lepton Flavor Universality + Violation}", + journal = "Phys. Rev.", + volume = "D96", + year = "2017", + number = "5", + pages = "055008", + doi = "10.1103/PhysRevD.96.055008", + eprint = "1704.05435", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + SLACcitation = "%%CITATION = ARXIV:1704.05435;%%" +} +@article{Hurth:2017hxg, + author = "Hurth, T. and Mahmoudi, F. and Martinez Santos, D. and + Neshatpour, S.", + title = "{Lepton nonuniversality in exclusive + $b{\rightarrow}s{\ell}{\ell}$ decays}", + journal = "Phys. Rev.", + volume = "D96", + year = "2017", + number = "9", + pages = "095034", + doi = "10.1103/PhysRevD.96.095034", + eprint = "1705.06274", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "CERN-TH-2017-110, IPM-P.A-466, MITP-17-035", + SLACcitation = "%%CITATION = ARXIV:1705.06274;%%" +} +@article{Bobeth:2017vxj, + author = "Bobeth, Christoph and Chrzaszcz, Marcin and van Dyk, + Danny and Virto, Javier", + title = "{Long-distance effects in $B\to K^*\ell\ell$ from + Analyticity}", + year = "2017", + eprint = "1707.07305", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "EOS-2017-01, MIT-CTP-4918, TUM-HEP-1087-17, ZU-TH-17-17", + SLACcitation = "%%CITATION = ARXIV:1707.07305;%%" +} +@article{Blake:2017fyh, + author = "Blake, Thomas and Egede, Ulrik and Owen, Patrick and + Pomery, Gabriela and Petridis, Konstantinos Alexandros", + title = "{An empirical model of the long-distance contributions to + $\bar{B}^{0} \rightarrow \bar{K}^{*0}\mu^{+}\mu^{-}$ + transitions}", + year = "2017", + eprint = "1709.03921", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + SLACcitation = "%%CITATION = ARXIV:1709.03921;%%" +} +@article{Hurth:2017sqw, + author = "Hurth, T. and Langenbruch, C. and Mahmoudi, F.", + title = "{Direct determination of Wilson coefficients using + $B^0\to K^{*0}\mu^+\mu^-$ decays}", + journal = "JHEP", + volume = "11", + year = "2017", + pages = "176", + doi = "10.1007/JHEP11(2017)176", + eprint = "1708.04474", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "CERN-TH-2017-178, MITP-17-053", + SLACcitation = "%%CITATION = ARXIV:1708.04474;%%" +}